A circle with circumference $6\pi$ has an arc with a $240^\circ$ central angle. What is the length of the arc? ${6\pi}$ ${240^\circ}$ $\color{#DF0030}{4\pi}$
Solution: The ratio between the arc's central angle $\theta$ and $360^\circ$ is equal to the ratio between the arc length $s$ and the circle's circumference $c$ $\dfrac{\theta}{360^\circ} = \dfrac{s}{c}$ $\dfrac{240^\circ}{360^\circ} = \dfrac{s}{6\pi}$ $\dfrac{2}{3} = \dfrac{s}{6\pi}$ $\dfrac{2}{3} \times 6\pi = s$ $4\pi = s$